Cost of War

Noah McGhee

Introduction

War and conflict are costly endeaevors. Primarily, the loss of life can not be neglected, however, in this study we will focus on the cost of militirization and how changes in militray spending relate to engagement in conflict. Using data from the Stockholm International Peace Reasearch Institute and the Department of Peace and Conflict Reaearch at Uppsala University in Sweden, information regarding military expenditure and conflict tracing, respectively, we will explore the relationship between them. The data was spliced by common years (1961-2018) and organized by country. Militay expenditure is in current USD.

A Look at the Data

Here is an example of the compiled data. This shows the first 5 years of data from Russia.

##              country year in_conflict mil_exp_usd   delta_exp per_in_conflict
## 1 Russian Federation 1993           1  7766720078          NA        5.172414
## 2 Russian Federation 1994           1 13547871733  5781151655        6.896552
## 3 Russian Federation 1995           1 12741629470  -806242263        8.620690
## 4 Russian Federation 1996           1 15826340652  3084711182       10.344828
## 5 Russian Federation 1997           0 17577353181  1751012529       10.344828
## 6 Russian Federation 1998           0  7955730401 -9621622780       10.344828

And here is another example of the same data from China.

##   country year in_conflict mil_exp_usd   delta_exp per_in_conflict
## 1   China 1989           0 11403453020          NA        22.41379
## 2   China 1990           0 10085081567 -1318371453        22.41379
## 3   China 1991           0  9953641758  -131439809        22.41379
## 4   China 1992           0 12420300875  2466659117        22.41379
## 5   China 1993           0 12577165930   156865055        22.41379
## 6   China 1994           0 10050586559 -2526579371        22.41379

A quick analysis of the variables yields the following…

(in_conflict) describes whether the country was engaged in conflict during that year with a (0) representing no, and a (1) representing a yes.

(mil_exp_usd) is the amount of currency, converted to US dollars the country spent of it’s military that year.

(delta_exp) is the change in the amount spent on a country’s military compared to the year prior.

(per_in_conflict) is the percent of year in conflict since the start of the data (1961). This value is being used as an analogue for likelihood of conflict.

Exploring the Data

Below are a few examples of some satistics from the data such years in conflict as well as average military expenditure over the time period.

##       country   mean_exp years_with_exp_data years_in_conflict   logexp
## 1 Afghanistan  154266784                  21        23.8669951 18.85419
## 2     Albania  113124907                  27         0.0000000 18.54400
## 3     Algeria 2541227046                  56         8.1077586 21.65591
## 4      Angola 1710053570                  41        21.7165685 21.25979
## 5   Argentina 2590972643                  57         4.6034483 21.67530
## 6   Australia 8766347738                  58         0.2711058 22.89419

Histogram of the log of miltary expenditure

Histogram of years in conflict

Next, we will take a look at a comparison a of a few countries. The first graph will be of the miltary expenditure ovber the years, overlaid with whether the country is was in conflict.

United States

Afghanistan

France

Applying Linear Regression

The variables of the model are as follows…

(per_in_conflict) - outcome variable is the percent of year in conflict since the start of the data (1961).

(country) - explanatory variable country.

(delta_exp) - explanatory variable is the change in the amount spent on a country’s military compared to the year prior.

(mil_exp_usd) - explanatory variable is the amount of currency, converted to US dollars the country spent of it’s military that year.

(mil_exp_usd^2) - explanatory variable the square of mil_exp_usd.

The results of the model…

## # A tibble: 108 × 5
##    term               estimate std.error statistic  p.value
##    <chr>                 <dbl>     <dbl>     <dbl>    <dbl>
##  1 (Intercept)        4.62e+ 1  2.70e+ 0     17.1  1.04e-63
##  2 I(mil_exp_usd^2)  -3.24e-22  2.83e-23    -11.4  6.52e-30
##  3 mil_exp_usd        3.12e-10  2.00e-11     15.6  2.57e-53
##  4 delta_exp         -1.65e-10  6.61e-11     -2.50 1.25e- 2
##  5 countryAlbania    -4.62e+ 1  3.51e+ 0    -13.2  6.65e-39
##  6 countryAlgeria    -3.25e+ 1  3.11e+ 0    -10.5  2.53e-25
##  7 countryAngola     -7.87e+ 0  3.25e+ 0     -2.42 1.55e- 2
##  8 countryArgentina  -3.88e+ 1  3.10e+ 0    -12.5  2.74e-35
##  9 countryAustralia  -4.83e+ 1  3.09e+ 0    -15.6  1.21e-53
## 10 countryAzerbaijan -3.22e+ 1  3.51e+ 0     -9.18 6.63e-20
## # ℹ 98 more rows

The equation of the model…

per_in_conflict = B_0 + B_1 * (mil_exp_usd^2) + B_2 * (mil_exp_usd) + B_3 * (delta_exp) + B_4… * country_1…

Where each beta after B_3 is country specific

For example, the equation for India would look like…

India : per_in_conflict = 46.21122 + -3.235196e-22 * (mil_exp_usd^2) + 3.118672e-10 * (mil_exp_usd) - 1.652636e-10 * (delta_exp) + -9.156034 * (1)

Inference for Regressioin

Below we will look at a few of the p values from the model as well as confidence intervals
## # A tibble: 6 × 4
##   term              p.value  conf.low conf.high
##   <chr>               <dbl>     <dbl>     <dbl>
## 1 (Intercept)      1.04e-63  4.09e+ 1  5.15e+ 1
## 2 I(mil_exp_usd^2) 6.52e-30 -3.79e-22 -2.68e-22
## 3 mil_exp_usd      2.57e-53  2.73e-10  3.51e-10
## 4 delta_exp        1.25e- 2 -2.95e-10 -3.57e-11
## 5 countryAlbania   6.65e-39 -5.31e+ 1 -3.94e+ 1
## 6 countryAlgeria   2.53e-25 -3.86e+ 1 -2.64e+ 1

All of the p values from the model are below the threshold of .05, therefore we ca reject the null hypothesis that states, there is no correlation between military expenditure, it’s change, country, and its percent of years involved in conflict.

Residual Analysis

Histogram of residuals from the model

Scatterplot of residuals from the model

Conclusion

Overall, the model does find a way to capture a portion of the story regarding war and money. Primarily, we think of spending on a military force to be the product of conflict however we must also loo at it through the lens that a powerful and well funded military is a deterrent for other countries to prompt you with war. Below, we will analyze some benefits and potential problems of the model.

Results

Given the p-values of the regression being sufficiently low this model can relatively accurately predict the likelihood that a country is currently in state of conflict. That being said, there is a complex phenomenon appears on the scatterplot of residuals that is telling of an unaccounted for behavior in the model. While there are many other factors that play a role in deciding whether a country is engaged in conflict it has shown that how much money and being placed into the military budget of a country is correlated with their involvement in conflict.

Limitations

Some key limitations of the study mostly surround the data. Data that accurately characterizes the kinetics of a country are difficult to produce and verify. That being said, the outcome variable used in the analysis could potentially be misleading to the state the country is in. The current outcome variable of percent in conflict assumes that hostility or volatility is a enduring trait and does not account for peaks of peace.